Symbolic Logic Problem : Sentence to Expression

Transcribe the English argument below into an appropriate logical language adequate to determine it to be valid. Also, please provide a derivation of the conclusion from the premises within the same logical system (by which you transcribed it). *this seems to be predicate logic and probably requires universal and existential quantifier. For universal use (X). Existential, use (E).

Every mental state is identical with some brain state or other. All mental states are introspectable. There is at least one mental state. Hence, some brain state is introspectable.

Solution Preview

Well, the first part is "Every mental state is identical with some brain state or other". We can write it as:

(X)(MX--->(EY)(BY & X=Y))
where X and Y are universal and M shows the mental state and B shows the brain state and X=Y means those two are identical.

Then we have: "All mental states are introspectable." which means:
(X)(MX--->IX)
where I means introspectable.